AdVenture Capitalist: I Like Big Numbers & I Cannot Lie

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All of these are numbers I encounter on a daily basis, thanks to my habit of leaving AdVenture Capitalist [official site] running in the background, but a few days ago they suddenly prompted me to actually think about the numbers and their names rather than letting them drift past, sextillions expanding into septillions, into octillions, nonillions and beyond – far beyond anything we encounter in real life.

At some point the numbers on the screen in AdVenture Capitalist stop making sense in the traditional numerical way. Their descriptors become these alien words which you stop being able to parse quickly. You can stop and unpick them given a few moments and a grounding in Latinate prefixes if you want to – quattuorquadraginta telling you forty-four is somehow involved, but they no longer trip off the tongue or easily fall into place in the brain.

Quattuorquadragintillion mean there are fourty-four sets of three zeroes beyond the initial thousand. So one quattuorquadragintillion is…

It’s a useless number in many ways. If your grocery shopping ever involves a quattuorquadragintillion something has gone so horrifically wrong with the economy that grocery shopping as we know it is probably not even a reality anymore. In fact, one of the interesting things about number systems is how we adapt them to stretch beyond what we usually need them for – how we wriggle them around to cope with the very big and the very small as knowledge changes or science advances.

AdVenture Capitalist is actually the first time I’ve encountered a quattuorquadragintillion by that name, but not the first time I’ve encountered awkwardly large numbers on the same scale. That’s because there are a few different ways of stretching our number systems to deal with bigness. I think the one AdVenture Capitalist uses is the Conway-Wechsler System.

I’m more familiar with indices when it comes to big numbers. In maths and science we learned standard form notation where, if we needed to write a large number we would put it in the form a x 10y. A is a number between 1 and 10 and then the y tells you how many places to move the decimal point. You go right if y is a positive number and left if it’s negative so you can write very big or very small numbers and get a sense of how they relate to one another without getting bogged down in writing out zeroes. A quattuorquadragintillion would be 1 x 10135.

The useful thing about standard form is that you can then use it to more easily perform calculations because you’re dealing with those superscript numbers – the indices – rather than all the zeroes, or trying to conceptualise what these words with strings of prefixes and an -illion mean.

In terms of general writing I don’t think I’ve ever meaningfully needed to use anything higher than a trillion and that’s only been with business reporting. But when I do – or if I need to use a billion – I remember learning about long and short scale notation. Both came out of France but one deals with powers of one million (hence a billion being a million million in long form) and the other is more concerned with thousands (so a billion in short form is a thousand million). I learned long form because that predominated in the UK until maybe half a century ago and it was the form one of my primary school teachers had learned. Short form is the standard generally when it comes to business and calculations but I do always try to check.

I’m also attached to long form purely sentimentally, because there’s something important-feeling about a million million. It feels like a more noteworthy achievement and makes billions delightfully rare as words and as collections of things.

Long form then uses the same salad of prefixes and -illions as you find in AdVenture Capitalist but the expansion is slower because it’s peppered with things like “a thousand quattuorquadragintillion” instead of swapping to a new word for the collection of zeroes. There’s also another long scale option where thousand -illions are called -illiards instead. So a thousand quattuorquadragintillion would be referred to as a quattuorquadragintilliard.

But anyway, one of the other interesting things about both long and short form is that for either notation the biggest number that I think most people have heard of doesn’t actually turn up. A googol is 10100 but given both long and short scale only deal in multiples of three or six zeroes (so kind of both only really working in groups of three zeroes but you know what I mean) a googol isn’t actually a big deal in either of them. It’s just 10 duotrigintillion (short) or ten thousand sedecillion (long) or ten sedecilliard (Peletier).

The reason I started thinking about all of this was because I was wondering whether the existence of AdVenture Captalist, or something pop culture-y like it would lead to the adoption of one convention as a standard just through it becoming the version people are most familiar with. We don’t encounter these numbers anywhere else in our daily lives, and if we are working in STEM fields there are generally systems and prefixes in place for the quantities or units in question specifically (maths and chemistry have standard form notation, computing looks to megabytes, gigabytes, terabytes, petabytes…).

There’s actually an ongoing conversation about standardisation (although I’m guessing it just pootles along or rears up occasionally as there’s not a pressing concern to resolve the issue that I’m aware of) of how we talk about big numbers. One proposed solution which would remove confusion is scrapping all the Latinate ideas and switching to Greek naming conventions based on multiples of a thousand. So one thousand to the power of four (1,000,000,000,000) would be a tetrillion.

I think one of the reasons I’m fond of this idea is that it still manages to be very classical European-centric, just swapping Latin for Greek and still working from groups of three zeroes instead of tens. For me it’s got that awkward compromise of antiquity, and sort of metric but sort of also not wanting to quite be metric. It also keeps the “-illion” bit which is from Latin and Italian as per Chalkdust Magazine:

“The Latin mille for 1000—from which we get millennium (1000 years) and mile (1000 paces)—is thought to have come from pre-13th century Italian. As the Romans had no names for numbers larger than 100,000, the Italians added the ending -one to mille to make it larger: milione.”

There are others, though. Donald Knuth’s -yllion notation which starts to look like a homebrew library cataloguing system pretty quickly and which references Chinese number systems

Mostly I just wanted to talk about numbers and how I’m enjoying them flowing past me in AdVenture Capitalist. They’re slowly becoming more normal to me, yet there’s magic in the strangeness of them. I see quattuorquadragintillion and I think “here be dragons”.

22 Comments

No discussion about large numbers is complete without a mention of Graham’s Number, the largest number ever seriously used in a mathematical proof. A number so mindbogglingly huge, even trying to describe it in chains of powers, like ten to the power of a million to the power of a million, repeated a million times, is a futile endeavour.

You ask: “Do you like this X?”
“Yes” means the number is a high one, because truthtelling Pip would respond with her true feeling about that number while evil Pip wouldn’t like the high number but can only lie about that.
“No” means the number is low, for the same reasons.

More formally: The functions of both normal and evil pip would yield the same results for the same input when asked the question:
L = low numbers, H = high numbers, L∩H=Ø
p(x) : {{true, xϵH},{hate, xϵL}}
ep(x) : {{!false, i.e. true, xϵH},{!true, i.e. false, xϵL}}
(Let’s hope that this editor doesn’t swallow the special characters, so consider this a preliminary rant about the missing edit-feature)

I really like the German naming convention. It’s a sort of gapless long scale. You have your Million (10^6), Billion (10^12), Trillion (10^18), etc. That’s a million^1, a million^2, million^3 respectively, which makes the prefixes nice and sensible.

I wholly understand the depth of your fear. Consider then that the German system gives you not only the Sextillion, but also the Sextilliarde! Not only is it a thousand times more potent – it also hints at bringing all the skill and fine mastery you have at billards to where it matters most.

And even the Sextillion is a quadrillion times greater than the sextillion. It’s as if all those enlargement ads finally came true!

Errr…no, this has nothing to do with computing. The scale prefixes are in use in pretty much all of science, hence Kilograms, Megahertz, Gigawatt, Terabit and Micrometer, Nanosecond and so on.

If one looks to see what’s done differently bis-a-vis numbers in computing, it’s the use of base 2 numbers (binary) and its powers – 32 this, 64 that, 4096 of the other. Combined with the prefixes we get fun stuff like 64MB caches, 512 bit bus widths, 16GB RAM and so on.